Minor improvements to "Probability current"

2 files changed, 11 insertions, 8 deletions

diff --git a/latex/know/concept/probability-current/source.md b/latex/know/concept/probability-current/source.md
index 69faf0c..bffc599 100644
--- a/latex/know/concept/probability-current/source.md
+++ b/latex/know/concept/probability-current/source.md
@@ -1,9 +1,12 @@
+% Probability current
+
+
 # Probability current
 
-In quantum mechanics, the *probability current* expresses the movement
-of the probability of finding a particle. Or in other words, it treats
-the particle as a heterogeneous fluid with density $|\psi|^2$. Now, the
-probability of finding the particle within a volume $V$ is given by:
+In quantum mechanics, the *probability current* describes the movement
+of the probability of finding a particle at given point in space.
+In other words, it treats the particle as a heterogeneous fluid with density $|\psi|^2$.
+Now, the probability of finding the particle within a volume $V$ is:
 
 $$\begin{aligned}
     P = \int_{V} | \psi |^2 \dd[3]{\vec{r}}
@@ -66,7 +69,7 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-This states that probability is conserved, and is reminiscent of charge
+This states that the total probability is conserved, and is reminiscent of charge
 conservation in electromagnetism. In other words, the probability at a
 point can only change by letting it "flow" towards or away from it. Thus
 $\vec{J}$ represents the flow of probability, which is analogous to the
diff --git a/static/know/concept/probability-current/index.html b/static/know/concept/probability-current/index.html
index 7b7ac32..b256e52 100644
--- a/static/know/concept/probability-current/index.html
+++ b/static/know/concept/probability-current/index.html
@@ -4,7 +4,7 @@
   <meta charset="utf-8" />
   <meta name="generator" content="pandoc" />
   <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes" />
-  <title>Prefetch | source</title>
+  <title>Prefetch | Probability current</title>
   <link rel="icon" href="data:,">
   <style>
     body {
@@ -50,7 +50,7 @@
 </div>
 <hr>
 <h1 id="probability-current">Probability current</h1>
-<p>In quantum mechanics, the <em>probability current</em> expresses the movement of the probability of finding a particle. Or in other words, it treats the particle as a heterogeneous fluid with density <span class="math inline">\(|\psi|^2\)</span>. Now, the probability of finding the particle within a volume <span class="math inline">\(V\)</span> is given by:</p>
+<p>In quantum mechanics, the <em>probability current</em> describes the movement of the probability of finding a particle at given point in space. In other words, it treats the particle as a heterogeneous fluid with density <span class="math inline">\(|\psi|^2\)</span>. Now, the probability of finding the particle within a volume <span class="math inline">\(V\)</span> is:</p>
 <p><span class="math display">\[\begin{aligned}
     P = \int_{V} | \psi |^2 \dd[3]{\vec{r}}
 \end{aligned}\]</span></p>
@@ -94,7 +94,7 @@
         = - \pdv{|\psi|^2}{t}
     }
 \end{aligned}\]</span></p>
-<p>This states that probability is conserved, and is reminiscent of charge conservation in electromagnetism. In other words, the probability at a point can only change by letting it “flow” towards or away from it. Thus <span class="math inline">\(\vec{J}\)</span> represents the flow of probability, which is analogous to the motion of a particle.</p>
+<p>This states that the total probability is conserved, and is reminiscent of charge conservation in electromagnetism. In other words, the probability at a point can only change by letting it “flow” towards or away from it. Thus <span class="math inline">\(\vec{J}\)</span> represents the flow of probability, which is analogous to the motion of a particle.</p>
 <p>As a bonus, this still holds for a particle in an electromagnetic vector potential <span class="math inline">\(\vec{A}\)</span>, thanks to the gauge invariance of the Schrödinger equation. We can thus extend the definition to a particle with charge <span class="math inline">\(q\)</span> in an SI-unit field, neglecting spin:</p>
 <p><span class="math display">\[\begin{aligned}
     \boxed{